Unable to select more than one object in Edit Mode
Your question is a little unclear, but I think I know what you are looking for.

Edit mode allows you to modify the geometry of a single object. Edit mode is based on the selected object and allows direct modifications of the mesh of the selected object. This means that if no object is selected, you can't go into edit mode. This also means that adding meshes in edit mode adds disconnected edges and faces to the selected object, and does not add an independent object.

Object modes allows translation of different independent objects while almost all of the other modes in viewport allow manipulation of the selected object.

To point out some things; meshes can be separated from an object using "p" (either though selection, material, or loose parts), origins can be reset by right clicking and selecting set origin, and then selecting the option that applies to your situation, and edit mode can be quickly toggled using tab.

If you want to be able to edit the meshes of multiple objects at once, you have to switch out of edit mode for that object, select a new object, and then enter edit mode for the new object. I recommend watching some tutorials on youtube as they can do a great job of explaining how objects and meshes work in blender.